I have the greatest handshake ever*. I think you need to have a firm handshake, but not a hand crushing one, and you should vary it depending on the handshake of the other person. If there's is a bit weak, then you should weaken yours a bit to be considerate. If there's it a bit on the strong side, then you should strengthen yours to let them know that you aren't one to get walked over.
My handshake differs between men and women too. I always actually shake with men, but unless I'm made to by the way the woman shakes, then I'll do a slight head dip whilst lifting their hand a bit. Kind of reminiscent of ye olde dayes when people kissed the womans hand, except I don't take it far enough to be considered that way. :)
*STATEMENT MAY BE EXAGGERATED